TY - JOUR
T1 - Unstable structures definable in o-minimal theories
AU - Hasson, Assaf
AU - Onshuus, Alf
N1 - Funding Information:
A. Hasson’s work was supported by the EPSRC grant no. EP C52800X 1.
PY - 2010/4/1
Y1 - 2010/4/1
N2 - Let M be a dense o-minimal structure, N an unstable structure interpretable in M. Then there exists X, definable in Neq, such that X, with the induced N-structure, is linearly ordered and o-minimal with respect to that ordering. As a consequence we obtain a classification, along the lines of Zilber's trichotomy, of unstable {thorn}-minimal types in structures interpretable in o-minimal theories.
AB - Let M be a dense o-minimal structure, N an unstable structure interpretable in M. Then there exists X, definable in Neq, such that X, with the induced N-structure, is linearly ordered and o-minimal with respect to that ordering. As a consequence we obtain a classification, along the lines of Zilber's trichotomy, of unstable {thorn}-minimal types in structures interpretable in o-minimal theories.
UR - http://www.scopus.com/inward/record.url?scp=77950022872&partnerID=8YFLogxK
U2 - 10.1007/s00029-010-0018-y
DO - 10.1007/s00029-010-0018-y
M3 - Article
AN - SCOPUS:77950022872
SN - 1022-1824
VL - 16
SP - 121
EP - 143
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
IS - 1
ER -